1952 AMC 12 Problem 28

Question

In the table shown, the formula relating

x

and

y

is:

$x$	$1$	$2$	$3$	$4$	$5$
$y$	$3$	$7$	$13$	$21$	$31$

y=4x-1

y=x^3-x^2+x+2

y=x^2+x+1

y=(x^2+x+1)(x-1)

None of these

Look at the first and second differences of the

y

-values

The constant second difference

2

suggests a monic quadratic; test the listed quadratic

The successive differences of the

y

-values are

4,6,8,10,

whose successive differences are all

2.

Thus the data fit a monic quadratic. Substitution shows

y=x^2+x+1

gives

3,7,13,21,31

at

x=1,2,3,4,5,

respectively.

Thus, the correct answer is C.

Problem 28 in other years